[Python] 拉格朗日插值

#-*— coding:utf-8 -*-
#Program 0.3 Lagrange Interpolation
import matplotlib.pyplot as plt
import numpy as np
import scipy as np
import random

#随机生成10个介于（-255，255）的结点
def getdata():
	a = np.zeros(10, np.double)
	b = np.zeros(10, np.double)

	for i in range(len(a)):
		a[i] = np.random.uniform(-255, 255) #随机生成介于-255到255的数
		b[i] = np.random.uniform(-255, 255)

	return a, b

#x, y 为已知插值结点
x, y = getdata()

#xn为新的x值
def Lagrange(x, y, xn):
	ans = 0.0

	#两重循环实现插值
	for i in range(len(y)):
		t = y[i]
		for j in range(len(y)):
			if i != j:
				t *= (xn - x[j]) / (x[i] - x[j])
		ans += t
	return ans

#开始插值
xn = np.arange(-255, 255, 1)
yn = np.zeros(len(xn))

for i in range(len(xn)):
	yn[i] = Lagrange(x, y, xn[i])

plt.plot(x, y, 'r*') #已知结点
plt.plot(xn, yn, '-') #插值结果
plt.title('Lagrange Interpolation')
plt.show()